Is it possible to describe an algorithm for procedural generation of a puzzle map?

Question

Algorithms

Hello! There are puzzles of the type: "move the boxes so that they stand on the buttons." There is a two-dimensional map with n-number of boxes and the same number of buttons. For example, the game "Smart Loader", but in general I met many implementations. People come up with this method: "what if so", and try to solve it? Is it possible to create an algorithm for an automatic puzzle map with the arrangement of buttons and drawers? Of course with 100% resolution. Who has any ideas about this? Thank you in advance for your help.

Answer 1

In extreme cases, you can always generate an already solved map and move boxes on it according to all the rules of the game in reverse order. Only for interesting levels it will be necessary to choose some additional rules for these moves, so that the options are more difficult, and not shifting one box back and forth.
And you can also randomize and check the solvability. Then fix it up a bit.